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Option pricing in the moderate deviations regime

Author

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  • Peter Friz
  • Stefan Gerhold
  • Arpad Pinter

Abstract

We consider call option prices close to expiry in diffusion models, in an asymptotic regime (“moderately out of the money†) that interpolates between the well†studied cases of at†the†money and out†of†the†money regimes. First and higher order small†time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.

Suggested Citation

  • Peter Friz & Stefan Gerhold & Arpad Pinter, 2018. "Option pricing in the moderate deviations regime," Mathematical Finance, Wiley Blackwell, vol. 28(3), pages 962-988, July.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:3:p:962-988
    DOI: 10.1111/mafi.12156
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    Citations

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    Cited by:

    1. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    2. Liexin Cheng & Xue Cheng, 2024. "Short-Term Asymptotics of Volatility Skew and Curvature Based on Cumulants," Papers 2401.03776, arXiv.org, revised Nov 2024.
    3. Antoine Jacquier & Fangwei Shi, 2018. "Small-time moderate deviations for the randomised Heston model," Papers 1808.03548, arXiv.org.
    4. Jacquier, Antoine & Pannier, Alexandre, 2022. "Large and moderate deviations for stochastic Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 142-187.
    5. Archil Gulisashvili, 2018. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Papers 1808.00421, arXiv.org, revised Jun 2019.
    6. Martin Forde & Stefan Gerhold & Benjamin Smith, 2021. "Small‐time, large‐time, and H→0 asymptotics for the Rough Heston model," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 203-241, January.
    7. Jiang Hui & Xu Lihu & Yang Qingshan, 2024. "Functional Large Deviations for Kac–Stroock Approximation to a Class of Gaussian Processes with Application to Small Noise Diffusions," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3015-3054, November.
    8. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    9. Masaaki Fukasawa, 2020. "Volatility has to be rough," Papers 2002.09215, arXiv.org.
    10. Gulisashvili, Archil, 2020. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3648-3686.
    11. Omar El Euch & Masaaki Fukasawa & Jim Gatheral & Mathieu Rosenbaum, 2018. "Short-term at-the-money asymptotics under stochastic volatility models," Papers 1801.08675, arXiv.org, revised Mar 2019.

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